Explanation Given: The magnitude of component force, F 1 = 800 N . The magnitude of component force, F 2 = 600 N . The magnitude of component force, F 3 = 650 N . The angle between the magnitude of component forces F 1 and x axes is 60 ° . The angle between the magnitude of component forces F 2 and y axes is 45 ° . Show the magnitude of component of forces F 1 , F 2 and F 3 into x and y axis components as in Figure (1). Show the magnitude of resultant force F R into x and y axis components as in Figure (2). Conclusion: Express magnitude of component force F 1 along the x direction using Figure (1). ( F 1 ) x = F 1 cos 60 ° (I) Substitute 800 N for F 1 in Equation (I). ( F 1 ) x = 800 cos 60 ° = 400 N Express magnitude of component force F 1 along the y direction using Figure (1). ( F 1 ) y = F 1 sin 60 ° (II) Substitute 800 N for F 1 in Equation (II). ( F 1 ) y = 800 sin 60 ° = 692.82 N Express magnitude of component force F 2 along the x direction using Figure (1). ( F 2 ) x = F 2 sin 45 ° (III) Substitute 600 N for F 2 in Equation (II). ( F 2 ) x = 600 sin 45 ° = 424.26 N Express magnitude of component force F 2 along the y direction using Figure (1). ( F 2 ) y = F 2 cos 45 ° (IV) Substitute 600 N for F 2 in Equation (IV). ( F 2 ) y = 600 cos 45 ° = 424.26 N Use Figure (3) and find out the cos θ and sin θ . cos θ = 12 13 sin θ = 5 13 Express magnitude of component force F 3 along the x direction using Figure (1). ( F 3 ) x = F 3 cos θ (V) Substitute 650 N for F 3 , and 12 13 for cos θ in Equation (V). ( F 3 ) x = ( 650 ) 12 13 = 600 N Express magnitude of component force F 3 along the y direction using Figure (1). ( F 3 ) y = F 3 sin θ (VI) Substitute 650 N for F 3 , and 5 13 for sin θ in Equation (VI). ( F 3 ) y = ( 650 ) 5 13 = 250 N Express the magnitude of resultant force measured counterclockwise from the positive x axis using Figure (1). + → ( F R ) x = ∑ F x ( F R ) x = ( F 1 ) x − ( F 2 ) x + ( F 3 ) x (VII) Substitute 400 N for ( F 1 ) x , 424

Engineering Mechanics: Statics and Study Pack (13th Edition)

13th Edition

ISBN: 9780133027990

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Chapter 2.4, Problem 40P

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The magnitude of the resultant force FR measured counterclockwise from the positive x axis and its direction θ.

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Chapter 2.4, Problem 39P

Chapter 2.4, Problem 41P

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Chapter 2 Solutions

Engineering Mechanics: Statics and Study Pack (13th Edition)

Ch. 2.3 - Determine the magnitude of the resultant force...Ch. 2.3 - Determine the magnitude of the resultant force....Ch. 2.3 - Determine the magnitude of the resultant force and...Ch. 2.3 - Resolve the 30-lb force into components along the...Ch. 2.3 - Resolve this force into components acting along...Ch. 2.3 - along the v axis. Prob. F2-6 Ch. 2.3 - Determine the magnitude of the resultant force FR...Ch. 2.3 - If = 60 and F = 450 N, determine the magnitude of...Ch. 2.3 - If the magnitude of the resultant force is to be...Ch. 2.3 - Determine the magnitude of the resultant force FR...

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The magnitude of the resultant force F R measured counterclockwise from the positive x axis and its direction θ .

The magnitude of the resultant force FR measured counterclockwise from the positive x axis and its direction θ.

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